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Since I'm trying to understand why the electric field is null inside a charged conductor, and the explanation usually given is that "the charges rearrange themeselves in such a way as to nullify the electric field inside the conductor", what I need is an example of continuous charge distribution for which the electric field is null in a finite region.

If I consider the Poisson's equation inside a conductor, what I get by enforcing V = constant is that $\bigtriangleup V = 0$ and then $\rho=0$. So I'm confused

I would be happy to have an answer just for the case of a spherical region.

Or, you could provide a link to a mathematical proof for the existence of an equilibrium configuration for a set of charged particles constrained in a finite region

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  • $\begingroup$ There is no field in the interior of a uniformly charged spherical shell... $\endgroup$
    – Ben51
    Feb 15, 2021 at 20:22
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    $\begingroup$ The charge distribution in a perfect conductor is not continuous at the boundaries, so the Laplacian in Poisson's equation is not really meaningful there. $\endgroup$
    – Thorondor
    Feb 15, 2021 at 20:27

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